Eight years after a federal judge in Washington ordered tobacco companies to pay for an antismoking ad campaign, the judge on Monday approved a plan for executing that order.

Three of the largest tobacco manufacturers in the United States—Philip Morris USA Inc., R.J. Reynolds Tobacco Co. and Lorillard Tobacco Co.—will have to buy ads detailing the health risks of smoking from a fixed list of television networks and newspapers. U.S. District Judge Gladys Kessler rejected recent challenges from networks and advocates for newspapers and radio stations that were excluded from the list.